MAT286-2005Springns

# MAT286-2005Springns - MAT286 Final Exam May 9 2005 1...

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MAT286 Final Exam May 9, 2005 1. Integrate the following indefinite integrals: (a). Z 1 x 2 + 3 x - x 4 + sin( x ) - tan( x ) dx . (b). Z x 3 ( x 4 + 10 ) 1 4 dx 2. Evaluate the following definite integrals: (a). Z 2 0 x x 2 + 1 dx (b). Z 2 π 0 cos x 4 dx 1

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2 3. An object is moving along a line with acceleration a ( t ) = - 2 t 2 + t meters / hour 2 . Initially, its velocity is 1 meter / hour and its position on the line is at the 3 meter mark. (a). Find the velocity v ( t ) of the object at time t . (b). Find the position s ( t ) of the object at time t . 4. (a). Set up integral(s) for the area between the curves y = x 2 and y = 8 - x 2 . Make a sketch. Do NOT evaluate. (b). Set up integral(s) for the area between the curves y = x and y = x 3 . Make a sketch. Do NOT evaluate.
3 5. Evaluate the following indefinite integrals: (a). Z ( x + 1) sin(2 x ) dx (b). Z 2 x 2 e 2 x dx 6. A solid of revolution is formed by rotating about the x -axis the region bounded by the curve from y = x (4 - x 2 ) from x = 1 to x = 2. Find the volume of the solid.

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4 7. The total cholesterol level of a patient on a special diet and medication is approximately
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